How do you raise large numbers to a power in an end-to-end encryption algorithm?

Question

RSA

I watched a video about end-to-end encryption. The author explained everything quite clearly and I understood the meaning, but a question arose.
The picture shows the final part of receiving a response with end-to-end encryption. 89 - decrypted message. Numbers 1394 and 2011 obtained as a result of number calculations. In order to decrypt the message, it is enough to raise the number 1394 to the power of 2011 and divide by 3127 modulo. Everything seems to be fine, but in reality, in order to maintain a high level of confidentiality, you need to use huge numbers, and here the question arises - how can I raise a number of lengths, say 100 characters, to the power of a number of lengths also 100 characters.